<?php
/**
 * @title 337. 打家劫舍 III - 优化
 * @author start2004
 */

// ini_set("memory_limit", "128M");

class Solution {

    /**
     * @param TreeNode $root
     * @return Integer
     */
    function rob($root) {
        /**
         * @since 2021-08-31 缓存, 避免重复计算
         */
        $this->dpArray = [];

        /**
         * @return
         */
        return self::find($root, 0);
    }

    /**
     * @title 返回最大值
     * @author start2004
     * @since 2021-08-31 Created
     *
     * @param TreeNode $root
     * @param int $key
     * @return int
     */
    function find($root, $key = 0){
        if($root === null){
            return 0;
        } elseif(isset($this->dpArray[$key])) {
            return $this->dpArray[$key];
        }

        /**
         * @since 2021-08-31 左右子树序号
         */
        $leftKey = ($key<<1)+1;
        $rightKey = $leftKey+1;

        /**
         * @since 2021-08-31 更下一层子树序号
         */
        $leftLeftKey = ($leftKey<<1)+1;
        $leftRightKey = $leftLeftKey+1;
        $rightLeftKey = $leftLeftKey+2;
        $rightRightKey = $leftLeftKey+3;

        /**
         * @since 2021-08-31 左子树存在
         */
        if($root->left !== null){
            $dpLeft = self::find($root->left, $leftKey);
            $dpLeftNext = self::find($root->left->left, $leftLeftKey) + self::find($root->left->right, $leftRightKey);
        } else {
            $dpLeft = $dpLeftNext = 0;
        }

        /**
         * @since 2021-08-31 右子树存在
         */
        if($root->right !== null){
            $dpRight = self::find($root->right, $rightKey);
            $dpRightNext = self::find($root->right->left, $rightLeftKey) + self::find($root->right->right, $rightRightKey);
        } else {
            $dpRight = $dpRightNext = 0;
        }

        /**
         * @since 2021-08-31 求最大值
         *
         * dp(root)=max(dp(left)+dp(right),num[root]+dp(left−left)+dp(left−right)+dp(right−left)+dp(right−right))
         */
        $result = max($dpLeft + $dpRight, $root->val + $dpLeftNext + $dpRightNext);

        /**
         * @return
         */
        $this->dpArray[$key] = $result;
        return $result;
    }
}



/**
 * @url http://127.0.0.1/leetcode/202008/2020.08.05_7.php
 */
$datas = [
    [3,2,3,null,3,null,1], // 7
    [3,4,5,1,3,null,1], // 9
    [1,2,3,4,5], // 12
    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];

include_once dirname(__DIR__) . DIRECTORY_SEPARATOR ."xhprof.php";
$xhprof = new Xhprof();
foreach ($datas as $data){
    // var_dump($data);

    $obj = new Solution();
    $result = $obj->rob($xhprof->tree($data));
    var_dump($result);
    echo str_repeat("<br>", 3);
}
$xhprof->end();
